The table given below shows the cost price and value of profit of 6 articles. Which of the following statement is NOT correct? I. The profit of D, E and F is 30.63 percent of the cost price of G, H and I. II. The ratio of total cost price to the total profit is 1 ∶ 2.Articles Cost price Profit D 700 200 E 600 150 F 400 300 G 500 400 H 300 250 I 800 350
Understanding the Profit and Cost Price Data
The question asks us to analyze the provided table containing the cost price and profit for six different articles (D, E, F, G, H, I). We need to evaluate two statements based on this data and determine which of them is/are incorrect.
Let's first look at the data presented in the table:
| Articles | Cost price | Profit |
|---|---|---|
| D | 700 | 200 |
| E | 600 | 150 |
| F | 400 | 300 |
| G | 500 | 400 |
| H | 300 | 250 |
| I | 800 | 350 |
Now, let's analyze each statement provided in the question.
Analyzing Statement I: Profit Percentage Calculation
Statement I says: "The profit of D, E and F is 30.63 percent of the cost price of G, H and I."
To verify this statement, we need to perform two calculations:
- Calculate the total profit of articles D, E, and F.
- Calculate the total cost price of articles G, H, and I.
- Calculate the percentage of the total profit of D, E, F with respect to the total cost price of G, H, I.
Step 1: Total profit of D, E, and F
Profit of D = 200
Profit of E = 150
Profit of F = 300
Total Profit (D, E, F) = \(200 + 150 + 300 = 650\)
Step 2: Total cost price of G, H, and I
Cost price of G = 500
Cost price of H = 300
Cost price of I = 800
Total Cost Price (G, H, I) = \(500 + 300 + 800 = 1600\)
Step 3: Calculate the percentage
Percentage = \(\frac{\text{Total Profit (D, E, F)}}{\text{Total Cost Price (G, H, I)}} \times 100\%\)
Percentage = \(\frac{650}{1600} \times 100\%\)
Percentage = \(\frac{65}{160} \times 100\%\)
Percentage = \(\frac{13}{32} \times 100\%\)
Percentage = \(0.40625 \times 100\% = 40.625\%\)
The calculated percentage is 40.625%. The statement claims it is 30.63 percent. Since 40.625% is not equal to 30.63%, Statement I is NOT correct.
Analyzing Statement II: Ratio Calculation
Statement II says: "The ratio of total cost price to the total profit is 1 ∶ 2."
To verify this statement, we need to perform two calculations:
- Calculate the total cost price of all 6 articles (D, E, F, G, H, I).
- Calculate the total profit of all 6 articles (D, E, F, G, H, I).
- Determine the ratio of total cost price to total profit.
Step 1: Total cost price of all articles
Total Cost Price = Cost price (D) + Cost price (E) + Cost price (F) + Cost price (G) + Cost price (H) + Cost price (I)
Total Cost Price = \(700 + 600 + 400 + 500 + 300 + 800\)
Total Cost Price = \(1300 + 400 + 500 + 300 + 800\)
Total Cost Price = \(1700 + 500 + 300 + 800\)
Total Cost Price = \(2200 + 300 + 800\)
Total Cost Price = \(2500 + 800 = 3300\)
Step 2: Total profit of all articles
Total Profit = Profit (D) + Profit (E) + Profit (F) + Profit (G) + Profit (H) + Profit (I)
Total Profit = \(200 + 150 + 300 + 400 + 250 + 350\)
Total Profit = \(350 + 300 + 400 + 250 + 350\)
Total Profit = \(650 + 400 + 250 + 350\)
Total Profit = \(1050 + 250 + 350\)
Total Profit = \(1300 + 350 = 1650\)
Step 3: Calculate the ratio of total cost price to total profit
Ratio = Total Cost Price ∶ Total Profit
Ratio = \(3300 \ratio 1650\)
We can simplify this ratio by dividing both numbers by their greatest common divisor. Notice that 3300 is exactly double of 1650 (\(1650 \times 2 = 3300\)).
Ratio = \(\frac{3300}{1650} \ratio \frac{1650}{1650}\)
Ratio = \(2 \ratio 1\)
The calculated ratio of total cost price to total profit is 2:1. The statement claims the ratio is 1:2. Since 2:1 is not equal to 1:2, Statement II is NOT correct.
Conclusion on Statement Correctness
Based on our analysis:
- Statement I is NOT correct (Calculated percentage is 40.625%, not 30.63%).
- Statement II is NOT correct (Calculated ratio is 2:1, not 1:2).
The question asks which statement is NOT correct. Since both statements are incorrect, the correct answer is that both I and II are not correct.
Revision Table: Key Calculations
| Calculation | Value | Based on |
|---|---|---|
| Total Profit (D, E, F) | 650 | Table Data |
| Total Cost Price (G, H, I) | 1600 | Table Data |
| Percentage Profit (D,E,F) of CP (G,H,I) | 40.625% | Calculated |
| Total Cost Price (All Articles) | 3300 | Table Data |
| Total Profit (All Articles) | 1650 | Table Data |
| Ratio (Total CP : Total Profit) | 2 ∶ 1 | Calculated |
Additional Information: Profit, Cost Price, and Ratios
Understanding the terms and concepts used in this problem is crucial for solving similar questions. Here's a brief overview:
- Cost Price (CP): This is the original price at which an article is bought or manufactured.
- Profit: Profit occurs when the selling price (SP) of an article is greater than its cost price (SP > CP). Profit is calculated as Profit = SP - CP. In this problem, the profit value is directly given.
- Profit Percentage: Profit percentage is usually calculated with respect to the cost price unless otherwise specified. It is given by the formula: Profit Percentage = \(\frac{\text{Profit}}{\text{Cost Price}} \times 100\%\). Statement I calculates a percentage of profit with respect to a different set of cost prices, which is a specific type of comparison.
- Ratio: A ratio is a comparison of two quantities by division. It shows how much of one quantity there is compared to another. A ratio of a:b can be written as a/b or a:b. Simplifying ratios involves dividing both parts by their greatest common divisor.
- Data Interpretation: Questions like this require careful reading of the table data and the statements, identifying the specific numbers and articles involved in each calculation, and performing the arithmetic accurately.
Paying close attention to which articles are mentioned in each statement (e.g., D, E, F for profit vs. G, H, I for cost price in Statement I) and what quantities are being compared (profit vs. cost price, total cost price vs. total profit in Statement II) is key to avoiding errors.
Important Questions from Bar Graph and Line Graph
The table given below shows the cost price and selling price of 5 different articles.
Article Cost price Selling price A 500 600 B 700 750 C 600 800 D 400 700 E 300 800 What is the ratio of total cost price to total selling price of all articles?
A ________ is often drawn as a guide, so that a frequency polygon can be drawn over the top.
Directions:
These data are based on the bar graph and line graph.
The following bar graph gives the total population of five cities(A, B, C, D and E) and number of females in the cities.
The following line graph gives the percentage of literates among females for each cities
Find the number of males in city B.
Directions:
These data are based on the bar graph and line graph.
The following bar graph gives the the total population of five cities(A, B, C, D and E) and number of females in the cities.
The following line graph gives the percentage of literates among females for each cities.
Find the number of females who is illiterate from city C.
Directions:
These data are based on the bar graph and line graph.
The following bar graph gives the total population of five cities(A, B, C, D and E) and number of females in the cities.
The following line graph gives the percentage of literates among females for each cities.
Find the number of females who are literate from city A.
